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D2001 #16860698

order4002
automorphismAut(G) order 2465232
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD2001
unambiguous semidirect productC3⋊D667
unambiguous semidirect productC23⋊D87
unambiguous semidirect productC29⋊D69

Splittings

Fitting, socle, derived, HallC3×C23×C29 ⋊ C2
HallC23×C29 ⋊ D3
HallC3×C29 ⋊ D23
HallC3×C23 ⋊ D29
SylowC29 ⋊ D69
SylowC23 ⋊ D87
SylowC3 ⋊ D667

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C23×C29C2
LCSG ▷ C3×C23×C29
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 2001

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(2,3)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Polycyclic presentation:

2,3,23,29|b^a=b^2,c^a=c^22,d^a=d^28

Conjugacy classes & character table

1002 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD6003, C3⋊D2001, C3×D2001, …
maximal normal subgroup ofC3×D2001, C5×D2001, C7×D2001, …
maximal quotient ofD6003, C3⋊D2001, C3×D2001, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4002, 8);